This paper tests the hypothesis that real per capita income growth rates are random walks against the hypothesis implied by models of endogenous growth that they are stationary. Thereby the influence of the choice of different test statistics as well as the choice of the H0 on the test results is analysed. As the results show, the overwhelming majority of countries rejects the random walk hypothesis in favour of the stationarity hypothesis, no matter what statistics and H0 is chosen. Additional tests show that growth rates of most countries significantly differ. Together with the stationarity result, this implies widespread and persistent divergence of real per capita incomes.